This is an alternating addition series with a random number, 4, interpolated as every third number. In the main series, 1 is added, then 2 is added, then 1, then 2, and so on.
Two patterns alternate here. The first pattern begins with 10 and adds 2 to each number to arrive at the next; the alternating pattern begins with 34 and subtracts 3 each time.
EXAMIANS